Model vault-reveal-fixed-1, 2 November 2026. Virtual-credit prototype. Not laboratory-certified or approved for real-money use.
| Outcome | Gross / original bet | Exact probability | Probability |
|---|---|---|---|
| No triple | 0× | 43991251/100000000 | 43.99125100% |
| Cash | 1.5× | 22638839/50000000 | 45.27767800% |
| Bonds | 2× | 3721689/50000000 | 7.44337800% |
| Gold | 3× | 2200029/100000000 | 2.20002900% |
| Handgun | 5× | 107/12500 | 0.85600000% |
| Diamond | 10× | 14479/6250000 | 0.23166400% |
Exact without-replacement terminal-state dynamic programming, independently cross-checked by exhaustive enumeration of every aggregated full-board arrangement for each inventory. Distinct filler-label permutations have equal multiplicity and cannot form a triple; all their paths are included by aggregation.
| Metric | 0 Keys in board | 1 Key in board | 2 Keys in board | Combined |
|---|---|---|---|---|
| RTP | 24/25 = 96% | 24/25 = 96% | 24/25 = 96% | 24/25 = 96% |
| Hit frequency | 56.00874900% | 56.00874900% | 56.00874900% | 56.00874900% |
| Net-win frequency | 56.00874900% | 56.00874900% | 56.00874900% | 56.00874900% |
| SD per original bet | 1.0190924811 | 1.0190924811 | 1.0190924811 | 1.0190924811 |
| Maximum gross / net | 10× / +9× | 10× / +9× | 10× / +9× | 10× / +9× |
| Exact 10× probability | 14479/6250000 | 14479/6250000 | 14479/6250000 | 14479/6250000 |
Variance: 207709897/200000000. Hit means positive gross return. All positive prizes exceed the stake. The 0/1/2-Key columns mean the inventory fixed at round creation; they do not mean the number of Keys actually found.
The server samples Key inventory 0/1/2 with probabilities 83%/15%/2%. It then chooses one of six inventory families using the exact ticket counts below. The no-triple family has balanced ordinary counts (2,2,2,2,1), (2,2,2,1,1) or (2,2,1,1,1), with uniformly shuffled symbol labels. Each symbol family contains six copies of that symbol, 3 minus the Key count distinct other symbols, and the chosen Keys. Finally all nine positions are uniformly shuffled. Inventory selection is not a promised win: a 0-Key symbol family wins with probability 37/42; a 1/2-Key symbol family wins with probability 1. Symbols are correlated and not independent draws.
| Keys | No triple | Cash | Bonds | Gold | Handgun | Diamond | Total |
|---|---|---|---|---|---|---|---|
| 0 | 1347632542 | 1901662476 | 312621876 | 92401218 | 35952000 | 9729888 | 3700000000 |
| 1 | 43991251 | 45277678 | 7443378 | 2200029 | 856000 | 231664 | 100000000 |
| 2 | 43991251 | 45277678 | 7443378 | 2200029 | 856000 | 231664 | 100000000 |
Start with five picks. Each Key consumes one pick and grants TWO picks: replacement plus one net extra reveal. Up to two Keys exist, at random fixed positions. Physical limits are 5/7/9 tiles for 0/1/2 Keys found. Two Keys can allow all nine tiles to be opened unless a triple ends play first. A Key shown only after settlement grants nothing. There is no bonus purchase, bonus stake or independent free-bonus RTP.
| Keys in board | Inventory probability | First 5 physical tiles contribution | Extension contribution | Full-round RTP |
|---|---|---|---|---|
| 0 | 83.00000000% | 24/25 | 0/1 | 96.00000000% |
| 1 | 15.00000000% | 148/175 | 4/35 | 96.00000000% |
| 2 | 2.00000000% | 148/175 | 4/35 | 96.00000000% |
Combined first-five contribution: 823/875; extension contribution: 17/875. Contributions are expected gross return divided by the original bet, not separate RTPs.
Grouping completed rounds by Keys actually found creates selection bias. Those conditional averages are not separately advertised RTPs:
| Keys found | Group probability | Conditional mean return / original bet |
|---|---|---|
| 0 | 91.28019998% | 68000000/70061557 = 97.05750616% |
| 1 | 7.99097085% | 44064000000/50343116351 = 87.52735864% |
| 2 | 0.72882917% | 2592000000/4591623793 = 56.45061784% |
| Band | Exact probability | Probability |
|---|---|---|
| 0 | 43991251/100000000 | 43.99125100% |
| (0,1) | 0/1 | 0.00000000% |
| [1,2) | 22638839/50000000 | 45.27767800% |
| [2,3) | 3721689/50000000 | 7.44337800% |
| [3,5) | 2200029/100000000 | 2.20002900% |
| [5,10) | 107/12500 | 0.85600000% |
| [10,infinity) | 14479/6250000 | 0.23166400% |
Display theme vault-loot-1: Cash 1.5×, Bonds 2×, Gold 3×, Handgun 5×, Diamond 10×. Only names and artwork changed; stable storage codes and every numerical probability/payout are retained. The Handgun is a stylized loot icon, not an interaction mechanic.
The complete board is sampled and uniformly permuted once, before the first selection. Conditional on any revealed history, every unopened position is exchangeable. Therefore any adaptive choice of an unopened position has the same next-symbol distribution as sampling without replacement. The rules require completion until the first triple or exhaustion of picks, including server auto-completion. Induction over the finite tree proves identical return distributions for all position-selection policies. No hint, optional purchase or early cashout changes that tree. Layouts are correlated inventories, not independent symbol draws.
After SETTLED with zero payout, the server may return the actual remaining fixed symbols. The client marks them Not played. They were present before the first selection, are shown for information only, and do not change payouts, picks, Keys or balance. No new symbols are sampled after loss. No almost-win result is manufactured. Winning and active rounds never receive this disclosure. The probability of losing on a board that contains an available triple is 4648726167/74000000000 (6.28206239% of all rounds); this is separate from winning probability.
| Seed | Rounds | Observed RTP | SE (percentage points) | z-score | |z| ≤ 3 |
|---|---|---|---|---|---|
| 0x51a7c0de | 100000000 | 95.97728400% | 0.01019092 | -2.229042 | PASS |
| 0x20261024 | 100000000 | 96.00960300% | 0.01019092 | 0.942309 | PASS |
| 0xc0ffee42 | 100000000 | 95.98230150% | 0.01019092 | -1.736692 | PASS |
Three predefined xoshiro128** seeds; exact rejection sampling and the production inventory/shuffle sampler. Every round evaluates the actual shuffled board with independent matching/pick logic. Simulation confirms the exact proof; it never replaces it. Failed z-scores are not removed or reseeded.
Unchanged USD ladder: 0.02, 0.10, 0.20, 0.50, 1.00, 2.00, 5.00, 10.00, 20.00, 25.00, 50.00, 100.00, 200.00, 500.00. Even minor-unit bets keep all 1.5× prizes integral, including currencies with 0, 2 and 3 decimals. Maximum stake $500, gross $5,000. After 10 minutes without an accepted reveal or 30 minutes total, the server completes remaining picks against the same board and settles; worker scheduling may delay presentation. Old sequential rounds retain their original version and original engine. Real-device Android/iPhone acceptance, wallet integration, independent security/math and regulatory review remain separate release gates.
From vault-reveal: npm run math (100M rounds × 3 seeds; 300M total, fails if |z| > 3). Full exact fractions, terminal paths, simulation and source SHA-256.